Center for Computational Medicine in Cardiology - News

Course on Mathematical Cardiac Physiology (starting October 23, 2019)

2019-10-18T10:36:04+02:00

We are very pleased to announce and course open for PhD and Master's students on Mathematical Cardiac Physiology. The course, starting on October 23, 2019 is taught by Dr. Simone Pezzuto (ICS, CCMC) and will cover advanced mathematical and numerical aspects of cardiac modeling. The room is SI-015, time is 13:30.

Background

The heart is an extraordinary organ. Its ultimate function is rather simple: to pump the blood throughout the body to supply oxygen and nutrients to the cells. How such functionality is achieved is however remarkably complex and poses significant challenges from a modeling and computational perspective. An electric stimulus, originating in the heart and indipendently from the central nervous system, travels across the heart to orchestrate and direct the mechanical contraction and relaxation, which in turn determine the pumping function.

From a clinical viewpoint, the job of a cardiologist is to study the patho-physiology of the heart, which in fact is the study of electric disorders (cardiac electrophysiology) and mechanical disfunction. In the heart, electric and mechanical function are tightly coupled: an electric disease (e.g., atrial fibrillation, tachycardia, bundle branch block) impedes a correct mechanical function which results into a pathological and potentially dangerous situation. Similarly, a mechanical or circulatory problem (hypertension, ischemia, infarct) can affect the electric function and lead to a vicious feedback affecting the overall functionality.

Diagnostically, the electrocardiogram (ECG) is a simple yet powerful tool to detect electric anomalies. Nonetheless, the ECG has acknowledged limitations, being hard to interpret in some situations also by a experienced cardiologist. ECG recording with high spatial coverage---the body surface potential mapping (BSPM), a vest composed by more than 200 electrodes---can significantly improve the diagnostic power, but they are difficult to summarize. In the so-called inverse problem of electrophysiology, these data is used to reconstruct the electric activity of the heart, enabling non-invasive diagnosis and therapy planning.

Mathematical modeling of cardiac electrophysiology is well established and already reaching the stage of clinical application. Commercial tools for solving the inverse problem of electrophysiology (ECG mapping) are nowadays available. Patient-specific modeling for optimal therapy delivery is, however, still in its infancy. One limitation is that current ECG mapping approaches is that they are imaging tools, without providing any valuable information to individualize patient-specific models. Another limitation is that being able to fix the electric pathology may not fix the mechanical function, which is ultimately the most relevant one. This is why coupled electro-mechanical models have started to emerge and being considered for in silico therapy planning.

The aim of this course is therefore to review these two important aspect of cardiac modeling: the inverse problem of electrophysiology, covered in the first part, and cardiac mechanics, in the second part. The inverse problem of electrophysiology comes in several flavors, each with its own benefits and idiosyncrasies. In the first lecture, after reviewing some basic facts of the ECG, we will study the modeling aspects of each formulation, their mathematical characterization as an inverse problem and the numerical solution strategy. In the second lecture, we will cover inverse problems in a more general sense, showing why they are illposed and the consequence of this. Regularization is a standard approach to alleviate the illposedness, but it does not come for free. A concept of optimal regularization (in the sense of Pareto optimality) will be introduced.

The second part of the course is devoted to cardiac mechanics or, more broadly, tissue mechanics. Biological materials usually undergo large deformations, hence the geometrical description of kinematics is more complex and constitutive assumptions are genuinely nonlinear. Additionally, biological tissues, and specifically the cardiac tissue, are anisotropic. After reviewing the introductory concepts of continuum mechanics in the third lecture, we will focus on hyperelastic materials and the well-posedness of the equilibrium formulation. Weaker concepts of convexity, polyconvexity and rank-one convexity, are introduced, which are more suitable for continuum mechanics. The fourth lecture will also cover the numerical discretization, which particular emphasis on how to deal with the incompressibility constraint. The last lecture will shift the focus on inelastic behavior arising from the electro-mechanical coupling or from growth and remodeling of the heart. The concept of active materials and multiplicative decomposition is studied and applied to relevant examples.

If time permits, a third part on the fluid-structure interaction (FSI) problem is planned. The heart is an extremely efficient mechanical pump, capable of working effectively at high-pressure regime (systolic pressure) as well as low-pressure regime (diastolic pressure). FSI is particularly relevant for the valves: these thin structures embedded in the blood control the inflow and outflow from the ventricles very efficiently.

Schedule

23/10/2019
This lecture is devoted to get familiar with the basic concepts of the *electrocardiogram* (ECG) and the inverse problem of electrocardiology.
A brief historical perspective from Einthoven's seminal studies will be proposed. The ECG is the manifestation of the electric activity of the heart, and nowadays can be accurately detected on the chest with high temporal resolution. A quite natural question is whether is possible to reconstruct the cardiac activity from such measures. In mathematical terms, this problem represents an *inverse problem*. In the lecture we will formalize the forward and inverse problem, and sketch solution strategies. Multiple formulations have been proposed, based on the extracellular potential, the transmembrane potential or the activation map. Each formulation has pros and cons.
30/10/2019
Illposedness of inverse problems. Interpretation. Regularization strategies. Tichonov, truncated SVD. KKT. Adjoint problem. Solution of the KKT system and preconditioning. Regularization in time.
06/11/2019
Brief introduction to continuum mechanics. Kinematics. Clausius-Duhem inequality and hyperelastic materials. Coleman's formalism and conjugated variables. Objectivity. Symmetries and invariants. Transversely isotropic materials. Incompressibility.
13/11/2019
Well-posedness, rank-one convexity, quasi-convexity, polyconvexity. Why full convexity of strain energy density function is not good. Lack of uniqueness: bifurcation. An example with Mooney-Rivlin material. Discretization and numerical solution. Three-field formulation, static condensation. Continuation methods. Why hexahedral grid are better than tetrahedral grids in computational mechanics?

20/11/2019
Active materials. Multiplicative decomposition and scale separation. Example application: tumour growth, morphogenesis, electro-mechanical coupling.
27/11/2019
Boundary conditions and coupling to systemic circulation. Fluid-structure interaction problem. Solution strategies.
04/12/2019
Valves. Immersed boundary method.
9-10/12/2019
TRM forum.
11/12/2019
Lab session.

References

Keener J., Sneyd J., Mathematical Physiology. Cambridge university press, 2009
Colli Franzone et al., Mathematical Cardiac Electrophysiology. Springer, 2014
Katz, A.M., Physiology of the Heart, Lippincott W&W, 2010

9TH TRM FORUM ON COMPUTER SIMULATION OF CARDIAC FUNCTION

2017-06-11T23:45:40+02:00

Final program here

Seminar Inter-subject variability in cardiac electrophysiology: Insights from experimentally-calibrated computer models

2017-05-09T12:04:34+02:00

24 October 2014, 14:30. Seminar Inter-subject variability in cardiac electrophysiology: Insights from experimentally-calibrated computer models by Professor Blanca Rodríguez, Oxford University. USI Lugano Campus, room A-24, Red building. Abstract

Seminar Sampling Signals with Finite Rate of Innovation: Theory and Biomedical Applications

2017-05-09T12:04:06+02:00

3 December 2014, 10:30. Seminar Sampling Signals with Finite Rate of Innovation: Theory and Biomedical Applications by Dr Pina Marziliano, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. USI Lugano Campus, room SI-007, Informatics building. Abstract

13th meeting on iMaging And eLectrical Technologies

2017-05-09T12:03:40+02:00

30 April - 1 May 2015 13th meeting on iMaging And eLectrical Technologies hosted by CCMC. Event websiteThe MALT meeting is a round-table conference focusing on the correlation of electrocardiography and cardiac imaging. The conference is a yearly event organized by an international study group, comprising, among others, biomedical engineers, cardiologists, and physiologists. All sessions are plenary, and consist of in-depth presentations and discussions with time slots of 30 minutes. Presentations are given by junior researchers (as a rule of thumb, those who have not yet obtained a PhD), while their advisers are encouraged to attend the meeting.The MALT meeting 2015 will be organized by organized by the Center for Computational Medicine in Cardiology, a joint institute of Università della Svizzera Italiana and Cardiocentro Ticino. The local organizing committee consists of Dr. Mark Potse, Prof. Dr. Rolf Krause, and Prof. Dr. Angelo Auricchio. For more information please visit the web page of the MALT meeting.

CCMC/Simula FOMICS Summer school on computational modeling of the heart

2017-05-09T12:03:18+02:00

24 - 28 August 2015 CCMC/Simula FOMICS Summer school on computational modeling of the heart Event website

8th TRM Forum on Computer Simulation and Experimental Assessment of Cardiac Function

2017-05-09T12:02:52+02:00

6 - 8 December 2015 8th TRM Forum on Computer Simulation and Experimental Assessment of Cardiac Function hosted by CCMC. Event website

1st annual meeting – MuTaLig COST Action

2017-05-09T12:02:28+02:00

21 - 22 July 2016 1st annual meeting – MuTaLig COST Action, hosted by Università della Svizzera Italiana. Event websiteThe first MuTaLig COST Action annual meeting will be organized as a joint Management Committee (MC) and Early Carrier Investigator (ECI) meeting. Selected renown experts in the multi-target drug discovery field will be invited. The purpose of this appointment is to stimulate collaborations among the participants in the research theme of multi-targeting and poly-pharmacology.

Research and Education in Computational Science and Engineering

2017-05-09T12:01:58+02:00

Report from a workshop sponsored by the Society for Industrial and Applied Mathematics (SIAM) and the European Exascale Software Initiative (EESI-2)
Research and Education in Computational Science and Engineering arXive page PDF

Prof. Vittorio Limongelli was designated as a most meritorious runner-up of the 2017 EFMC

2017-05-09T11:55:23+02:00

Prof. Vittorio Limongelli was designated as a most meritorious runner-up of the 2017 EFMC (the European Federation of Medicinal Chemistry) Prize for a Young Medicinal Chemist in Academia. The EFMC Prize will be conferred on occasion of the 7th edition of the EFMC International Symposium on Advances in Synthetic and Medicinal Chemistry (EFMC-ASMC’17), which will be held in Vienna, Austria, August 27-31, 2017. Event website